Half side formula - Alchetron, The Free Social Encyclopedia

In spherical trigonometry, the half side formula relates the angles and lengths of the sides of spherical triangles, which are triangles drawn on the surface of a sphere and so have curved sides and do not obey the formulas for plane triangles.

Formulas

The half-side formulas are

tan ⁡ ( a 2 ) = R cos ⁡ ( S − A ) tan ⁡ ( b 2 ) = R cos ⁡ ( S − B ) tan ⁡ ( c 2 ) = R cos ⁡ ( S − C )

where

a, b, c are the lengths of the sides respectively opposite angles A, B, C,

S = 1 2 ( A + B + C ) is half the sum of the angles, and

R = − cos ⁡ S cos ⁡ ( S − A ) cos ⁡ ( S − B ) cos ⁡ ( S − C ) .

The three formulas are really the same formula, with the names of the variables permuted.

References

Half-side formula Wikipedia

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